Information in Games.

Abstract

In the first chapter, we tightly bound from the outside the set of sequential equilibrium payoffs in repeated games of private monitoring. To do this, we develop a tractable new solution concept for standard repeated games with perfect monitoring: Markov Perfect Correlated Equilibrium generalizes the operator approach of Abreu, Pearce and Stacchetti (1990), but instead takes correlated equilibrium of the auxiliary game. We show that for any private monitoring structure, the set of sequential equilibrium payoffs of a repeated game is contained within the set of Markov Perfect Correlated Equilibrium payoffs.

The second chapter extends the Blackwell comparison of experiments to a strategic setting. We introduce a new partial order more strategically informative --- information held by players is "better'' --- and prove it is equivalent to the partial order more strategically valuable --- the ability to induce more equilibrium payoff vectors in all Bayesian games. The centerpiece application is to repeated games with private monitoring where the more strategically informative order ranks monitoring structures. Consequently, we can show when a change in monitoring structure will weakly expand the set of sequential equilibria.

The third chapter deals with the tragedy of the commons. When effort imposes negative externalities, competition results in excessive aggregate effort. One way to curb these excesses is for subsets of competitors to form groups which share output or gross revenue. In theory, if the right number of groups forms, Nash equilibrium aggregate effort should fall to the socially optimal level. We investigate experimentally whether individuals manage to form the efficient number of groups and to invest within the chosen groups as theory predicts. Although we observe some systematic departures from theory, we find that subjects vote in most cases to divide themselves into the optimal number of output-sharing groups and, when investing within such groups, curtail inefficiency by 50% to 71%.